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In Shapley, the marginal contribution of a feature is computed by comparing the performance of a model with and without a feature over all possible subsets of features.

A common choice is using the average value of a feature, when such feature is not present in the selected subset.

What would be the implication of using a fixed constant value for a missing feature (e.g., a reference point) instead of its average value?

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Most probably it will introduce a bias in the estimation of Shapley value. However on average this should not pose a problem.

Taking the average value (ie arithmetic mean) of a feature, over a given dataset, in no way guarantees that is the most probable or characteristic value, unless the distribution is of a specific kind (eg normal).

So taking another reference point might introduce bias, but on average given random means, it should not pose a problem.

The above is a deduction not a detailed analysis.

References:

  1. A Unified Approach to Interpreting Model Predictions
  2. Shapley value
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  • $\begingroup$ are the properties of shapley satisfied only when conditional expectation is used? $\endgroup$
    – zzzbob
    Jun 7 at 18:22
  • $\begingroup$ Taking the average value (ie arithmetic mean) of a feature over a given dataset, in no way guarantees the expected value unless the distribution is of specific kind. So taking another reference point might introduce bias but on average given random means it should not pose a problem. Is my analysis. $\endgroup$
    – Nikos M.
    Jun 7 at 18:48

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